Question
Factorize the following expressions:
$64 a^3-b^3$
$64 a^3-b^3$
✓
Answer
$64 a^3-b^3$
$=(4 a)^3-b^3$
$=(4 a-b)\left((4 a)^2+4 a \times b+b^2\right)$
$\therefore\left[a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]$
$=(4 a-b)\left(16 a^2+4 a b+b^2\right)$
$\therefore 64 a^3-b^3=(4 a-b)\left(16 a^2+4 a b+b^2\right)$
$=(4 a)^3-b^3$
$=(4 a-b)\left((4 a)^2+4 a \times b+b^2\right)$
$\therefore\left[a^3-b^3=(a-b)\left(a^2+a b+b^2\right)\right]$
$=(4 a-b)\left(16 a^2+4 a b+b^2\right)$
$\therefore 64 a^3-b^3=(4 a-b)\left(16 a^2+4 a b+b^2\right)$
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